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Erschienen in:
2015 | OriginalPaper | Buchkapitel
7. Elementary Sheaf Theory
verfasst von : Demeter Krupka
Erschienen in: Introduction to Global Variational Geometry
Verlag: Atlantis Press
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Abstract
The purpose of this chapter is to explain selected topics of the sheaf theory over paracompact, Hausdorff topological spaces. The choice of questions we consider are predetermined by the global variational theory over (topologically nontrivial) fibered manifolds, namely by the problem how to characterize differences between the local and global properties of the Euler–Lagrange mapping, between locally and globally trivial Lagrangians, and locally and globally variational source forms. To this purpose, the central topic we follow is the abstract De Rham theorem and its consequences. In particular, in the context of this book, the cohomology of abstract sheaves should be compared with the cohomology of the associated complexes of global sections, and the cohomology of underlying smooth manifolds.